Bibliographic Details
| Title: |
Balleans of topological groups. |
| Authors: |
Hernandez, Salvador1, Protasov, Igor2 i.v.protasov@gmail.com |
| Superior Title: |
Journal of Mathematical Sciences. Oct2011, Vol. 178 Issue 1, p65-74. 10p. |
| Subject Terms: |
*TOPOLOGICAL groups, *COMPACTIFICATION (Mathematics), *METRIC spaces, *TOPOLOGICAL spaces, *MATHEMATICAL analysis |
| Abstract: |
A subset S of a topological group G is called bounded if, for every neighborhood U of the identity of G, there exists a finite subset F such that S ⊆ FU, S ⊆ UF. The family of all bounded subsets of G determines two structures on G, namely the left and right balleans B( G) and B( G) , which are counterparts of the left and right uniformities of G. We study the relationships between the uniform and ballean structures on G, describe all topological groups admitting a metric compatible both with uniform and ballean structures, and construct a group analogue of Higson's compactification of a proper metric space. [ABSTRACT FROM AUTHOR] |
|
Copyright of Journal of Mathematical Sciences is the property of Springer Nature and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.) |
| Database: |
Academic Search Premier |